Theory and algorithms of the Laguerre transform, Part II: Algorithm

The Laguerre transform developed by Keilson, Nunn and Sumita provides an algorithmic framework for the computer evaluation of repeated combinations of various continuum operations such as multiple convolutions, integration, differentiation, and multiplication by polynomials. In the previous survey paper, the authors summarize theoretical results on the Laguerre transform obtained up to date. Following the theoretical summary, the aim of this paper is to discuss the operational characters of the Laguerre transform when actually using it in applications. The two summary papers will enable the reader to use the Laguerre transform with ease.